Interpolation and approximation for data living on manifold surfaces

Meshed surfaces are ubiquitous in digital geometry processing and computer graphics. The set of attributes associated with each vertex such as the vertex locations, curvature, temperature, pressure or saliency, can be recognized as data living on mani- fold surfaces. So interpolation and approximation for these data are of general interest. This paper presents two approaches for mani- fold data interpolation and approximation through the properties of Laplace-Beltrami operator （Laplace operator defined on a mani- fold surface）. The first one is to use Laplace operator minimizing the membrane energy of a scalar function defined on a manifold. The second one is to use bi-Laplace operator minimizing the thin plate energy of a scalar function defined on a manifold. These two approaches can process data living on high genus meshed surfaces. The approach based on Laplace operator is more suitable for manifold data approximation and can be applied manifold data smoothing, while the one based on bi-Laplace operator is more suit- able for manifold data interpolation and can be applied image extremal envelope computation. All the application examples demon- strate that our procedures are robust and efficient.

A real-time data smoothness method based on xPC-Target

A method of real-time data smoothness which is applied in a hardware-in-the-loop （HIL） simulation platform for a plug-in hybrid electric vehicle synthetical power device is described. The input signal of the platform comes from a AC/DC switch power with output containing noises. A linear slide average arithmetic is applied to smooth the noises. To average a certain number input sample signals, this method can decrease the noises voltage level, which meet the requirement of the simulation platform. The efficiency and signal delay time are presented to describe the result of this method, and a statistical index is used to judge the arithmetic＇ s efficiency. The tests results show that the arithmetic fit the requirement of the HIL simulation platform.

Analysis on residual strain of Zipingpu Concrete Faced Rockfill Dam after Wenchuan earthquake

The Zipingpu Concrete Faced Rockfill Dam （CFRD） was subjected to significant local damage in the ＂5.12＂ Wenchuan earthquake. It is the first rockfill dam of more than one hundred meters high to encounter a strong earthquake anywhere in the world. Based on the finite element smoothing method, the residual strains at a typical cross-section and a downstream slope of the dam were obtained by processing the dam monitored displacement data. The position of and reason for the dam settlement and deformation ofrockfill dilatancy in the earthquake were analyzed according to the section residual strain. The results show that the maximum settlement ratio on the dam body approximately occurs at 2/3 of the dam height; dilatancy occurs from the dam crest to 25-30 m in the upstream and downstream slope; the immediate cause of the face slabs horizontal construction joint dislocation is excessive residual shear strain. Meanwhile, the position of and reason for the dam fissure in the earthquake were analyzed according to the dam slope residual strain.

Dynamic single-index model for functional data

We propose a new functional single index model, which called dynamic single-index model for functional data, or DSIM, to efficiently perform non-linear and dynamic relationships between functional predictor and functional response. The proposed model naturally allows for some curvature not captured by the ordinary functional linear model. By using the proposed two-step estimating algorithm, we develop the estimates for both the link function and the regression coefficient function, and then provide predictions of new response trajectories. Besides the asymptotic properties for the estimates of the unknown functions, we also establish the consistency of the predictions of new response trajectories under mild conditions. Finally, we show through extensive simulation studies and a real data example that the proposed DSIM can highly outperform existed functional regression methods in most settings.